Dual object

In category theory, a branch of mathematics, it is possible to define a concept of dual object generalizing the concept of dual space in linear algebra.

A category in which each object has a dual is called autonomous or rigid.

Consider an object ${\displaystyle X}$ in a monoidal category ${\displaystyle (\mathbf {C} ,\otimes ,I,\alpha ,\lambda ,\rho )}$. The object ${\displaystyle X^{*}}$ is called a left dual of ${\displaystyle X}$ if there exist two morphsims

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